Research Journal of Applied Sciences, Engineering and Technology 4(7): 729-734, 2012
ISSN: 2040-7467
© Maxwell Scientific Organizational, 2012
Submitted: September 29, 2011
Accepted: November 04, 2011
Published: April 01, 2012
Modeling and Application of PMSG Based Variable Speed Wind
Generation System
S. Sajedi, H. Jafari Rezabeyglo, A. Noruzi, F. Khalifeh, T. Karimi and Z. Khalifeh
Ardabil Branch, Islamic Azad University, Ardabil, Iran
Abstract: In the early development of wind energy, the majority of wind turbines were operated at constant
speed. Recently, the number of variable-speed wind turbines installed in wind farms has increased and more
wind turbine manufacturers are making variable-speed wind turbines. In this study maximum power control
of wind turbine and permanent magnet synchronous generator connected with two back to back voltage source
converters to grid are studied. Machine currents are controlled by indirect vector control method. In this
method, generator side converter controls the maximum excitation (air gap flux) by machine's d-axis current
and controls generator torque by machine's q-axis current. PMSG speed is controlled by Tip Speed Ratio (TSR)
upon the wind speed variations to generate the maximum output power. Grid side converter regulates the DC
link voltage and injective active power by d-axis current and regulates the injective reactive power by q-axis
current using simple control method P-Q. Simulation results depict that the proposed method operates properly.
Key words: Boost converter, maximum power point tracking, wind energy conversion system
The power extracted by the wind is related to the
third order of wind speed. Applying power electronics
converters to transfer the power to grid with the
possibility of speed variation in a great range of values is
preferred because of their great advantages. Various
methods are presented to control the maximum power
where almost all of the efficient methods apply rotor
speed feedback (Spooner and Williamson, 1996;
Chinchilla et al., 2006; Senjyu et al., 2006). In this paper,
maximum power point tracking is executed by sampling
the rotor and wind speeds.
At first, it is described how to estimate the speed and
adaptive notch filter and then the controlling system of
power injection to grid and maximum wind power
extraction system are illustrated. Simulation results are
shown at the end of this study.
INTRODUCTION
Nowadays, among the all renewable energy sources,
wind systems are more economic in comparison with
others. Variable wind speed systems deliver 20% to 30%
more energy in compare with the constant speed systems.
They also decrease power oscillation and improve
reactive power injection (Kim and Kim, 2007; Weisser
and Garcia, 2005). Various technologies are developed for
wind systems as their application has developed. During
the previous years, PMSGs are greatly used in wind
turbine applications because of their advantages such as
low weight and velocity, high efficiency and gearless
structure (Spooner and Williamson, 1996; Chinchilla
et al., 2006). Extracting maximum power of turbine and
delivering an appropriate energy to grid are two important
purposes in wind turbines.
According to these purposes, AC-DC-AC structure is
the best structure to convert the power in wind turbines
(Spooner and Williamson, 1996; Chinchilla et al., 2006;
Arifujjaman et al., 2006; Hana et al., 2007). Figure 1
shows one of the most common structures applied for
PMSGs. This structure contains a full wave diode
rectifier, a DC-DC boost converter and a 3-phase inverter.
In this structure, inverter satisfies the requirements related
to grid connection and boost converter provides the ability
of extracting maximum power using DC bus control in
output of rectifier (Spooner and Williamson, 1996;
Chinchilla et al., 2006).
MATERIALS AND METHODS
The proposed system is consisted of five main parts:
Wind model, Wind Turbine, Boost converter and
superconductive inductor, Power injection to grid and
Maximum Wind Power Extraction. Theses parts have
discussed and finally the simulation results have been
introduced.
Wind model: The model applied for this simulation is
composed of three components and is described as follow
(Surgevil and Akp2nar, 2005):
Corresponding Author: S. Sajedi, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
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Res. J. App. Sci. Eng. Technol., 4(7): 729-734, 2012
Conventional DC Boost
Rectifier
Chopper
which can be defined as turbine power in proportion with
wind power and is related to blades aerodynamic
characteristics. Resulted mechanical torque is applied as
the input torque to the wind generator and makes
generator to operate. Power conversion factor is expressed
as the function of tip speed ratio λ as follow:
Inverter
PMSG
Grid
Cp = (0.44 − 0.0167β ) sin
Fig. 1: Wind turbine system with PMSG and boost converter
π ( λ − 2)
− 0.00184(λ − 2) β (5)
13 − 0.3β
where B is blade's pitch angle. For a turbine with constant
pitch, β is considered as a constant value, Fig. 2 is Cp
variations in terms of λ for different β -values. In this
paper β is considered zero where the cp value would be
0.48 then. Table 1 shows the wind turbine parameters
values applied in simulation.
Boost converter and superconductive inductor: Boost
converter stabilizes the voltage of DC link unrepentantly
from the output voltage of rectifier which is caused by
speed variation of synchronous generator. DC link voltage
is stabilized through regulating the boost converter switch
conduction ratio (D). D is the result of dividing the
conduction time of switch in each period by the switching
period. Stabilized DC link voltage in the inverter
terminals leads to efficiency increase and appropriate
exploitation of Power Semiconductor Devices. Boost
converter behaves like a second order system which has
an additional zero at the right side of imaginary axis.
Right side zero makes system to operate like a non
minimum phase system which is not desirable in voltage
regulators. Because of any variation in output voltage
might increase before being corrected by the controller.
As it is obvious in Fig. 3, the energy storage device plays
the main roll in the operation of boost converter. During
each switching period of DC converter and also during the
conduction time of switch, energy is stored in magnetic
field of inductor and then during the 2nd part of period
where the switch does not conduct, energy is injected to
the capacitor bank of DC link. If a superconductive
inductor is used to exchange the electromagnetic energy,
the ability of energy storing and the efficiency increases
greatly. These energy storage devices are commonly
applied to improve the dynamic behavior of power
systems and to correct the oscillations of industrial loads.
Specially when the system rating is not high, cost of using
high temperature superconductors have been reduced
obviously and the system have been economized nearly.
In order to compare, it should be noted that what is
presented in (Nomura et al., 2005) is the application of
systems with tens of MJ rating, but as what is proposed
Fig. 2: Cp in terms of 8 for different $-value
VWIND = VBASE + VGUST + VRAMP
(1)
where VBASE is the main component, VGUST is the gust
component and VRMP is the ramp component. The main
component is a constant speed. Ramp component can be
expressed by a sinusoidal function which is considered as
a composition of several different sinusoidal functions
and gust component is considered as storm and sudden
wind.
Wind turbine: The torque generated by wind blow is
described by the following relations (Karrari et al., 2005):
λ=
ωMR
VWIND
(2)
PM =
1
ρπR 2 C pV 3 WIND
2
TM =
PM
ωM
=
ω3
1
ρπR 5CP M3
2
λ
(3)
(4)
where VWIND is wind speed, R is the blades radius, P is the
air density, ω M is rotor angular speed and 8 is the Tip
Speed Ratio (TSR), Cp is the power conversion factor
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Res. J. App. Sci. Eng. Technol., 4(7): 729-734, 2012
Fig. 3: Configuration and control system of proposed wind energy system
Power injection to grid: In Fig. 3, inverter control
system to control the injected active and reactive powers
is shown. The relations of these powers in synchronous
reference frame are as follow (Nomura et al., 2005;
Knight and Peters, 2005):
P=
3
(vd id + vqiq )
2
(7)
Q=
3
(v i − vd iq )
2 qd
(8)
If synchronous reference frame is synchronized with
the grid voltage, the q-axis component of grid voltage will
be zero and power relations will be as follow:
Fig. 4: Maximum power of turbine in term of wind and rotor
speed
P=
here, the storing devices limit the rating of the systems
applied in boost converter to tens of KJ.
Natural frequency and damping ratio of boost
converter are computed as follow (Ang and Oliva, 2005):
ξ=
L
1
(1 − D)
,ω m =
C 2 R(1 − D)
LC
3
vd id
2
3
Q = − vd iq
2
(9)
(10)
According to the above relation, by controlling the
currents of d-axis and q-axis, active and reactive powers
can be controlled respectively. Two controlling loops are
used to control these currents. The outer loop of capacitor
voltage control is used to generate the d-axis reference
current. This control will end in transferring the total
generated power to grid. Q-axis reference current is
specified by desirable selecting the grid injected reactive
power. If unit power factor is considered, this current
would be regulated at zero value.
(6)
The above relation shows that a considerable increase
in L value reduces the frequency of system and decreases
the ripple components of state variables. At the other
hand, as L value increases, ∆I L (current ripple of
superconductive inductor) will decrease to the value in
which the operation of controlling system will face with
distortion. Thus, correct selection of superconductive
inductor will lead to an economic system in addition to all
advantages presented in (Nomura et al., 2005).
Maximum wind power extraction: Figure 4 shows the
relation between the output power of turbine and its speed
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Res. J. App. Sci. Eng. Technol., 4(7): 729-734, 2012
Table 1: Wind turbine parameters
WRated power
Blade radius
Nominal wind speed
Minimum wind speed
Maximum wind speed
Blade pitch angle
15k W
5.5 m
12 m/s
4 m/
18 m/s
0
Table 2: PMSG parameters
values
R
Lq
Ld
P
J
parameters
2.875 S
8.5 mHLq
8.5 mHLd
4
0.0008 Kg.m2
Fig. 5: DC voltage bus curve in term of optimum rotor speed
Table 3: Simulation parameters
values
Vi
Li
LDC
C1
C2
Fs
parameters
63.33 V
5 mHi
2 mH
2200 uF
2200 uF
10 kHz
s
Table 4: Controllers parameters
values
Kid
Kpd
Kiq
Kpq
Kic
Kpc
parameters
10
1
10
1
100
1
for different wind speeds. It is seen that the optimum rotor
speed is different in various wind speeds to obtain the
maximum power of turbine.
In PMSG, the relation between torque and inducted
voltage is as follow:
T = Kt I a
(11)
E = Keω
(12)
E 2 = V 2 + ( I aωLs ) 2
(13)
Fig. 6: DC voltage bus curve in term of optimum rotor speed
obtained simulation and approximation
where ω is the angular rotor speed and Ia is stator
current. In the other hand, it is obvious that:
Fig. 7: Simulated wind speed
where V is the terminal phase voltage and LS is the
inductance of generator. DC voltage at the output of
rectifier ( VDC) is as follow:
VDC =
3 6
π
In respect to the fact that the torque is determined by the
rotor and wind speeds, a specific voltage value is
estimated for a specific rotor and wind speed as relation
If DC voltage relation is obtained in terms of
optimum speed, resulted diagram would be as Fig. 6.
Now, a feedback from rotor speed, DC bus voltage can be
obtained through Fig. 6 and can be applied to the
systemBy applying this control, speed and voltage vary
continuously until they reach to their balance mode in a
point on the curve shown in Fig. 5. In this case, maximum
power of wind energy is obtained from the wind turbine.
(14)
V
which VDC according to the relations (11-14) is as follow:
VDC =
3 6
π
ω Ke2 − (
TLs 2
)
Kt
(15)
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Res. J. App. Sci. Eng. Technol., 4(7): 729-734, 2012
RESULTS AND DISCUSSION
In order to study the operation of proposed wind
turbine, the mentioned system is simulated using
MATLAB/SIMULINK software with the parameters of
Table 2, 3. Table 4 shows the parameters of controllers.
Figure 6 shows the DC voltage curve in terms of
optimum rotor speed. Mentioned curve is derived through
simulating system in various wind and rotor speeds. The
dotted line is a second order approximation of the above
curve which is used to control the maximum power in
coming simulations. Maximum and minimum rotor
speeds are considered 1.3 p.u and 0.6 p.u, respectively.
The proposed system is simulated for two seconds
with variable wind speed as shown in Fig. 7.
In Fig. 8 and 9 capacitor voltage and grid injected
reactive power are shown respectively. These two figures
show that the system has satisfied the requirements of grid
connection appropriately. Because the voltage level of
capacitor is kept constant and reactive power transition is
almost zero (unit power factor is considered here).
Figure 10 shows the electrical and mechanical power
curves. It is obvious that after a short period of time,
generated mechanical power of turbine tracks the
maximum mechanical power of turbine (considering the
wind speed). Also in Fig. 10, grid injected active
electrical power is shown which differs from the
generated mechanical power according to the electrical
and mechanical losses. As it is obvious, grid injected
power curve tracks the maximum power curve of the
turbine with about 0.1 sec delay time which is the result
of using PI controllers in controlling circuit of inverter.
Fig. 8: Capacitor voltage
Fig. 9: Injected reactive power to grid
CONCLUSION
As wind turbines develop, various technologies are
presented to improve their application. PMSG is under
attention of these technologies because of its special
abilities. In most PMSG wind systems, generated voltage
of the generator is converted into DC voltage through a
full-bridge diode rectifier and this voltage is controlled to
control the maximum power of turbine. The grid side
inverter is controlled by grid injected active and reactive
power control method. Simulation results show that the
maximum power is obtained from the turbines correctly
for different wind speeds and active and reactive powers
are injected to grid appropriately.
Fig.10: Injected ative power to grid, maximum mechanical
power of turbine
As it is obvious, Fig. 6 is a nonlinear curve. But it can
easily be applied using a linear approximation around the
nominal operation point. In this study a second order
approximation is used. Determining optimum DC voltage,
switching ratio of boost converter (D) is calculated to
reach this voltage.
D=
Vc − VDC −Re f
Vc
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